Gypsum is made up of interlocked and elongated crystals. The random nature of its morphology suggests to resort to homogenization of random media to investigate its mechanical properties from the scale of the single crystals upwards. Unfortunately, the usual homogenization schemes fail to quantitatively predict the influence of the porosity on the effective Young's modulus of gypsum. This is clearly due to the inability of such approaches to take into account the elongated nature of the crystals. A modification of the classical self-consistent scheme is proposed. It is validated against elastic characteristics computed by finite element analyses, and also against experiments on real dried gypsum samples with empty pores. Finally, a strength model based on brittle failure is presented. The whole strength domain in the space of macroscopic principal stresses is derived. The comparison to experimental data in both simple tension and simple compression is remarkably good.